基于修正的χ2-距离散度的不确定概率约束优化

Ambiguous probabilistic constrained optimization based on modified χ2-distance divergence

许多有重要价值的实际问题的数学模型为不确定性概率优化模型,如决策问题等,该类模型常存在分布的不确定性.研究了基于修正的χ2-距离散度的不确定概率优化问题,构造了基于修正的χ2-距离散度的不确定集,对模型内部极大化问题进行求解.研究了最坏情况下的概率函数,用测度变换的方法把一个关于分布P的优化问题转化为关于似然比(ξ)的凸优化问题;应用凸优化问题的对偶理论,证明了拉格朗日对偶问题的等价性,并且得到了不确定概率优化问题的等价形式.

Many practical problems with important values can be modeled as ambiguous probabilistic optimization problems ,such as decision making problem ,which often exist uncertainty distribution . This paper aims at studying ambiguous probabilistic optimization problems based on modified χ2‐dis‐tance divergence .First of all ,ambiguous set based on modified χ2‐distance divergence is constructed . Second ,the inner maximization problem of the models is solved .We study the worst‐case probability function .Applying the change‐of‐measure technique ,we convert an optimization problem with re‐spect to distribution P to a convex optimization problem with respect to LR （ξ） .Moreover ,equiva‐lence of Lagrange dual problems is proved by using the duality theory of convex optimization prob‐lem .Consequently ,we obtain the equivalent form of ambiguous probabilistic optimization problems .